Francis Bacon (1561-1626): The father of empiricism and Scientific Revolution

Francis Bacon (1561-1626) was an English scientist and lawyer. Bacon was an instrumental figure in the Renaissance and Scientific Enlightenment. In particular, Bacon developed and popularised a scientific method which marked a new scientific rigour based on evidence, results and a methodical approach to science. He is widely considered to be the father of empiricism and the Scientific Revolution of the Renaissance period.

Early life

Bacon was born 22 January 1561 near the Strand, London, England. Aged 12, he entered Trinity College, Cambridge where he followed a traditional medieval curriculum with most lessons conducted in Latin. Although he admired Aristotle, he was critical of Aristotle’s approach to philosophy (he called it ‘unhelpful’) and the scholastic tradition which was unquestioning in accepting past assumptions of the classic teachers, such as Aristotle and Plato.

Aged 15, Bacon travelled to the continent, spending time in France but also visiting Italy and Spain. He studied civil law and became acquainted with political realities, serving as part of England’s foreign ambassadors. On his travels, he delivered letters for high ranking English officials, including Queen Elizabeth I.

In 1579, the sudden death of his father meant Bacon returned home to London, where he began his practice of law at Gray’s Inn. With little or no inheritance, he was forced to borrow from family members to tide him over. Despite ill health, which dogged him throughout his life, Bacon was ambitious to serve his country, church and thirdly to pursue the truth – in philosophy and science.

In 1581, he was elected to Parliament as a member of Bossiney, Cornwall. He would remain a member of parliament (for different constituencies) for the next four decades. This provided a platform to help Bacon become a noted public figure and leading member of the government.

Bacon’s political views

Bacon was a liberal reformer. He supported the monarch within a parliamentary democracy. He supported reform of feudal laws and spoke in favour of religious tolerance. He was also an influential supporter of union between England and Scotland (which occurred 1707). He advocated the union on the grounds that a constitutional union would bring the nations closer together, promoting peace and economic strength.

His sharp intellect and grasp of issues saw him promoted to different posts, including Attorney General in 1594. He was also a skilful political operator, willing to flatter and beseech people of influence and power to help him gain favour.

However, after opposing Queen Elizabeth’s plan to raise subsidies for the war against Spain, he temporarily fell from favour and he struggled to find a position. His limited financial reserves came back to haunt him and, for a time, he was arrested for debt. However, he later regained the Queens trust and was part of the legal team which investigated charges against the Earl of Essex for a plot of treason against the Queen.

Bacon as Lord Chancellor

The ascension of James I, saw Bacon become one of the kings most trusted civil servants. He managed to mostly stay in favour with both the King and parliament – despite their estrangement over the Kings extravagance. Bacon was appointed Baron Verulam in 1618 and Lord Chancellor (the highest position in the land) in the same year. Bacon was the main mediator between the king and parliament during the tense years. By 1621, he was appointed to the peerage as Viscount St Alban. However, by the end of the year, his meteoric rise to the top of British politics came to an abrupt end as he was arrested for 23 counts of corruption. Bacon had fallen into debt, but also the charges were enthusiastically promoted by Sir Edward Coke, a lifelong enemy of Bacon.

Bacon argued the charges were promoted by political intrigue. Although he had accepted gifts, he claimed this was widely regarded as the custom of the day, and he never let it influence his decision. Writing to the king, he wrote:

“The law of nature teaches me to speak in my own defence: With respect to this charge of bribery I am as innocent as any man born on St. Innocents Day. I never had a bribe or reward in my eye or thought when pronouncing judgment or order… I am ready to make an oblation of myself to the King.”

— 17 April 1621

However, after a Parliamentary investigation, he admitted his guilt – perhaps hoping for a lenient sentence or perhaps feeling Parliament were determined to see his downfall whatever he said.

“My lords, it is my act, my hand, and my heart; I beseech your lordships to be merciful to a broken reed.”

Parliament though had little sympathy for Bacon and found him guilty. Bacon was fined £40,000, sent to the Tower of London and barred from holding future office.

After a few days in the Tower, he was released by King James and his fine overturned. But, his public fall could not be undone and Bacon would never return to parliament or public office.

Despite his fall from grace, Bacon responded with a prolific literary output; writing on a range of topics from science and philosophy to legal matters and Britain’s political situation. Bacon’s literary output and originality of thought were more remarkable given the backdrop of Sixteenth Century England. The religious and political tensions of the age had led to a period of limited philosophical inquiry. Bacon was an integral part of the English Renaissance, which saw a revitalisation of literature. Interestingly, Bacon has sometimes been suggested as the real author of the works of William Shakespeare, though this theory is not taken too seriously by scholars.

Scientific inquiry

It is this area of Bacon’s work that has been most influential. Bacon’s primary concern was to re-consider man’s approach to science. He rejected the assumptions of ‘innate knowledge’ and felt the duty of a scientist was to take a sceptical approach to any preconceptions, but only rely on the actual evidence and results of experiments. Bacon emphasised the importance of induction by elimination. Bacon also encouraged scientific progress through collaborative work.

Novum Organum (1620) was one of his most influential works, which expressed a new style of logic. Bacon advocated the use of reduction and empirical understanding. It rejected a more philosophical ‘metaphysical’ approach of the old sciences. Bacon invented the metaphor ‘idol’ to indicate how a man could be wrongly influenced by forces such as over-simplification, hasty generalisations or over-focus on meaningless language differences.

The importance of this scientific method is that it opened up the possibility for challenging all existing scientific orthodoxy. Bacon’s approach was championed by Voltaire, and it became a strong component of the French enlightenment. Modern science does not follow Bacon’s method in all detail, but the spirit of empirical research can be traced to Bacon’s revolutionary new approach.

Thomas Jefferson wrote: “Bacon, Locke and Newton. I consider them as the three greatest men that have ever lived, without any exception, and as having laid the foundation of those superstructures which have been raised in the Physical and Moral sciences”

Bacon was a hero to Robert Hooke and Robert Boyle the founders of the Royal Society.

Law

Bacon was prolific in suggesting reforms to English law. During his lifetime, few were accepted by the English legal system. However, after his death, some see Bacon’s general principles incorporated into modern legal systems, such as the Napoleonic Code and modern common law. The greatest contribution of Bacon was to place emphasis on the facts of the case, rather than a strict statement of legal precedent. Similar to his scientific empiricism, Bacon wanted the law to be more about the evidence and facts of the case, and not get caught up in obtuse legal precedents.

A criticism of Bacon is that he ordered five warrants for torture with regard to suspects accused of treason. Bacon argued torture could be justified, if necessary, to uncover plots of treason; though he did not admit it as useful for providing legal evidence.

Religion

Francis Bacon was a Protestant Christian, and his Christian faith was important to his outlook on life. However, his approach was broad-minded, seeing the role of rational scientific analysis. He generally advocated religious tolerance. He has been associated with the Rosicrucians – a mystical movement, which believed in a transformation of divine and human understanding. His work ‘New Atlantis’ expresses the ideals of a utopian community founded on spiritual laws and modern scientific rationalism. In this utopian land there is:

“generosity and enlightenment, dignity and splendour, piety and public spirit”

Bacon’s novel places a scientific institution, Solomon House, at the centre of the land, and remarks how the scientists seek to work in harmony with the Divine.

“We have certain hymns and services, which we say daily, of Lord and thanks to God for His marvellous works; and some forms of prayer, imploring His aid and blessing for the illumination of our labors, and the turning of them into good and holy uses.”

In 1609 he wrote De Sapientia Veterum (“The Wisdom of the Ancients”) which was an account of the hidden wisdom in ancient myths. It was one of his most popular books

“The most ancient times are buried in oblivion and silence: to that silence succeeded the fables of the poets: to those fables the written records which have come down to us.”

– Preface

It suggests Bacon’s sympathy to a more inclusive religious approach beyond the confines of modern Christianity.

Personal life

Aged 36, Bacon courted Elizabeth Hatton, but she broke off their relationship to marry Sir Edward Coke – a lifelong rival of Bacon’s.
Aged 45, Bacon married Alice Farnham, who at the time was just 14. The couple split, after disagreements over money. Bacon later disinherited Alice, after he discovered she had an affair with another man.

On 9 April 1926, Bacon died from pneumonia. In an account by John Aubrey, (‘Brief Lives’) Bacon died after catching a chill conducting a scientific experiment – trying to stuff a fowl with snow to see if it preserved life. Writing his last letter to Lord Arundel, Bacon also mentions this incident:

“…As for the experiment itself, it succeeded excellently well; but in the journey between London and Highgate, I was taken with such a fit of casting as I know not whether it were the Stone, or some surfeit or cold, or indeed a touch of them all three.”

Bacon was a revolutionary figure in constitutional law, science and philosophy. He sought to advocate new ways of dealing with the world. His radical approach to fundamental questions of life and the world we live in were influential for promoting a different spirit – the new age of reason and enlightenment. Bacon sought a synthesis between a rational scientific approach, but also with a spiritual understanding of a just society.

Citation: Pettinger, Tejvan. 

PUBLICATION: Omotoso Ibukunoluwa Omoniyi

Nicolaus Copernicus (1473 – 1543): The Polish / Prussian mathematician and astronomer

Nicolaus Copernicus (1473 – 1543)  – Polish / Prussian mathematician and astronomer. Copernicus created a model of the universe which placed the sun at the centre of the universe (heliocentrism) – challenging the prevailing orthodoxy of the time – which believed the earth at the centre of the universe.

His major work De revolutionibus orbium coelestium (1543) (On the Revolutions of the Celestial Spheres) was published just before his death and marked an important scientific landmark – it was a key moment in the scientific revolution of the Renaissance period.

As well as being a pioneering astronomer, Copernicus excelled in many different fields – he was a practising physician, economist, diplomat, scholar and gained a doctorate in canon law.

Early Life Copernicus

Copernicus was born 19 February 1473, in the city of Thorn in the province of Royal Prussia – the Kingdom of Poland. [Copernicus would likely have considered himself Prussian.] His father was a wealthy merchant, who was also politically active in supporting Poland against the Teutonic Order, and he played a leading role in peace negotiations between the two factions. His mother’s family were also very wealthy and influential making Copernicus well connected throughout his life.

After the death of his father, Copernicus was given a full education by his maternal uncle. Copernicus became prolific in several languages, including spoken Latin, German, Polish, Greek and Italian.  He studied at the Cathedral School at Wloclawek and the University of Krakow. Copernicus’ studies included astronomy and mathematics, Aristotelian philosophy and Aristotelian natural-sciences.

Copernicus supplemented his studies with his own private reading, including works by Euclid, Pythagoras, Plutarch, Ptolemy and many works related to astronomy.

In 1496, Copernicus left to the University of Bologne Italy, where he studied Canon Law with a view to a career in the church. After completing his studies, he temporarily succeeded to the Warmia Canonry. However, he was never fully ordained as a priest and turned away from Canon law – preferring the humanities which were of greater interest to him.

Copernicus also began making an increasing number of astronomical observations, such as the lunar eclipse of 1500. It was through his close studies and astronomical observations that he began to increasingly develop a different view of the Universe to which most people held at the time.

In addition, to these studies, he became a practising physicist and would perform operations on many significant people throughout his life.

In 1503, Copernicus returned to Poland where he served as secretary to his uncle who was the Prince-Bishop of Warmia. In this capacity, he also became involved in diplomatic negotiations over the ongoing tensions between Prussia and the Teutonic Order.

Religious beliefs

Copernicus was broadly supportive of the humanist movement, which sought to offer a more liberal approach to life, literature and the sciences. He printed translations of Greek literature, which showed his support for more a more liberal approach to non-Christian literature.

He felt his scientific studies and reading was fully compatible with being a good Catholic Christian; he also never showed any interest in the new Protestant Reformation movement. Copernicus believed the right attitude was to use his God-given reason and scientific method and not just rely on blind faith in scriptures. He writes in his preface to De revolutionibus

“ If perchance there should be foolish speakers who, together with those ignorant of all mathematics, will take it upon themselves to decide concerning these things, and because of some place in the Scriptures wickedly distorted to their purpose, should dare to assail this my work, they are of no importance to me, to such an extent do I despise their judgment as rash”

Heliocentric view of the Universe

After the death of his uncle, Copernicus moved to Frombrook, in the Kingdom of Poland where he continued to make more astronomical observations, such as viewing Mars, Saturn and the earth’s eccentricity in relation to the movement to the stars; he used fairly primitive instruments and telescopes in these observations. These observations continued to inform and develop his heliocentric view of the universe. He shared his radical ideas and observations in private letters but held back from publishing because he feared receiving criticism and scorn for his revolutionary new theories.

In 1532, Copernicus finished writing his life’s great work Dē revolutionibus orbium coelestium. The major points of the work included:

“The sun is not inappropriately called by some people the lantern of the universe, its mind by others, and its ruler by still others. The Thrice Greatest labels it a visible god, and Sophocles’ Electra, the all-seeing. Thus indeed, as though seated on a royal throne, the sun governs the family of planets revolving around it.”

1. There is no one centre of all the celestial circles or spheres.
2. The centre of the earth is not the centre of the universe, but only of gravity and of the lunar sphere.
3. All the spheres revolve about the sun as their midpoint, and therefore the sun is the centre of the universe.

He was very reluctant to publish, despite some favourable interest shown by friends and even the Pope and Catholic cardinals in the Vatican.

However, encouraged by friends, students and elements within the Church, he finally published in 1543, the year of his death. He died on 24 May 1543 – one story says that on the very day he died, he awoke from a coma to view his life’s work finally printed – before dying peacefully in his sleep.

Economics

Amongst his many achievements, Copernicus was also a pioneering economist. He developed a theory on the value of money (later became known as Gresham’s Law – the idea that bad (debased money) drives out good money. In 1517, he created the first attempt at a quantity theory of money – Inflation was related to the amount of money in circulation; this became a principal element of economic theory. It was important for that particular time period, where governments struggled with currency devaluation. His writings on economics became influential for both Prussia and Germany (Teutonic states).

Influence of Copernicus’ work

For sixty years after his death, only a small number of astronomers and intellectuals accepted Copernicus’s heliocentric viewpoint. However, on the publication of his thesis, there was little controversy and no real criticism from the church.

There were theological objections from leading figures in the Protestant Reformation, such as Martin Luther and John Calvin. The Protestant Reformation placed biblical scripture as the ultimate authority and rejected Copernicism for the perceived conflict with Biblical sources.

However, by 1616, more objections from Catholic church were being made. Members of the Inquisition, such as Francesco Ingoli wrote Copernicism was theologically heretical.

Galileo’s (1564-1642) work in astronomy made him come to the conclusion Copernicus was right. In particular, it was Galileo (with the use of improved telescopes) who found moons orbiting the planet Jupiter; this was a justification for Copernicus’ view. But as Galileo advanced the view of heliocentrism, he received considerable opposition from the Catholic Church, and he became convicted of heresy on the basis that heliocentrism was contrary to the sense and authority of Holy Scripture. Galileo was placed under house arrest for many years. But, Galileo played a key role in seeing heliocentrism accepted as scientific fact.

Copernicus’ De revolutionibus and Galileo’s Dialogue Concerning the Two Chief World Systems were placed on the Catholic Church’s prohibited list until 1835.

Copernican Revolution

The Copernican Revolution is said to be the period from 1543 to the time of Isaac Newton and his works on gravity.

Citation: Pettinger, Tejvan. 

PUBLICATION: Omotoso Ibukunoluwa Omoniyi

Leonardo da Vinci (1452 – 1519): one of the world’s greatest thinkers, artists and philosophers.

Leonardo da Vinci Biography

Leonardo da Vinci (1452 – 1519) is one of the world’s greatest thinkers, artists and philosophers. Seeking after perfection, he created rare masterpieces of art such as ‘The Mona Lisa’ and The Last Supper.’

In addition to art, Da Vinci studied all aspects of life from anatomy to mathematics and astronomy; his far-reaching investigations and discoveries sought to show an underlying unity of the universe. Da Vinci is considered to be a key person in the birth of the European Renaissance, which saw an emergence of new ideas, scientific discoveries and the creation of beautiful art.

Short Biography of Leonardo da Vinci

Leonardo was born an illegitimate son of a Florentine noble and peasant woman; he grew up in Vinci, Italy. In his formative years, he developed a love of nature and from an early age began to display his remarkable academic and artistic talents.

Adoration of the Magi by Da Vinci

In 1466, he moved to Florence where he entered the workshop of Verrocchio. Initially, his formative style reflected his teacher but he soon developed an artistic sense which went far beyond his master’s rigid style. His first work of significance was the “Adoration of the Magi” commissioned by monks of San Donato a Scopeto. Although unfinished, the work was a masterpiece and introduced several new ideas. In particular, he introduced themes of movement and drama. He also pioneered the use of Chiaroscuro; this is the technique of defining forms through the contrast of light and shadow. This would be later used to great effect in the Mona Lisa.

“Shadow is the means by which bodies display their form. The forms of bodies could not be understood in detail but for shadow.” The Notebooks of Leonardo da Vinci (Richter, 1888)

In 1482, Leonardo went to the court of Ludovico Sforza in Milan, where he stayed for 16 years. Here he continued painting and also branched out into other interest such as engineering and anatomy.  During this period he painted the famous artworks “Madonna on the Rocks” and also “The Last Supper.”

Last Supper by Leonardo Da Vinci

The Last Supper has been described as one of the greatest religious paintings. With Christ at the centre of the picture, it embodies great feeling and emotion as Christ is about to announce his imminent betrayal by Judas. The painting is held at the Convent of Santa Maria Delle Grazie, Milan, but unfortunately over time the quality of the original painting has deteriorated, despite frequent restoration attempts.

Leonardo Da Vinci and Mona Lisa

In 1499, his patron L. Sforza was defeated by the French invasion, causing Leonardo to return to Florence. During this period, he painted the fresco of the Battle of Anghiari. This artwork was to exert tremendous influence over future artists. However, it was never completed and was later destroyed. It was also during this period that Leonardo completed The Mona Lisa. The Mona Lisa is one of the world’s most famous and intriguing pictures. The Mona Lisa is a portrait of a wife of a Florentine noble. For several days she came to Leonardo and sat for her portrait to be painted; however, she refused to smile. Leonardo even tried hiring musicians but to no avail. One day, just for a fleeting second, she gave a faint smile, and Leonardo was able to capture it. Her smile encapsulates a mysteriousness which is both fascinating and intriguing. Sri Chinmoy said of the Mona Lisa.

“That smile has immortalized her, immortalized the artist and immortalized the art. Artist and art have been immortalized by just a faint smile, a smile that has an enigmatic touch. Even now a soul-touch is there, and that soul-touch has conquered the heart of the world.” (1)

In the Mona Lisa, Leonardo masters the techniques of sfumatoand chiaroscuro. Sfumato enables a gradual transition between colours – allowing delicate and expressive images. In the Mona Lisa, the use of chiaroscuro is evident in the contrast between her face and the dark background.

Glider design by Da Vinci

In this period Leonardo also extended his studies into engineering, science and other subjects. There seemed to be no end to his interests. He made copious notes in his complex mirror handwriting, much of which wasn’t deciphered in his lifetime. He also drew complex models of machines; in particular, he was fascinated by flight. He used to buy birds just so that he could release and enjoy watching them fly away. Da Vinci also attempted to build a flying object himself. Machines that he drew on paper, such as helicopters, would become a reality many centuries later. If his medicinal studies had been published, it would have revolutionised the science, as he was one of the first to understand the circulation of blood within the body. He also realised the earth revolved around the sun, anticipating the future work of Copernicus and Galileo.  Da Vinci was driven to contemplate all aspects of life and the world, it left him with a great love and fascination with the universe.

“Here forms, here colours, here the character of every part of the universe are concentrated to a point; and that point is so marvellous a thing … Oh! marvellous, O stupendous Necessity — by thy laws thou dost compel every effect to be the direct result of its cause, by the shortest path. These are miracles…” The Notebooks of Leonardo da Vinci

Through different fields, Da Vinci sought to see an underlying unity in the universe and took an optimistic view of human potential.

“Things that are separate shall be united and acquire such virtue that they will restore to man his lost memory.”

The Vitruvian Man

Leonardo Da Vinci’s Vitruvian Man

This is a drawing of the proportions of man. Da Vinci used earlier work and notes by the Roman architect Vitruvius. The picture combines art, man and science – illustrating the beauty of geometrical proportions and the human form. It is symbolic of Da Vinci’s work, and the Renaissance he inspired, to combine these art forms into one diagram. In the simplicity of a line drawing, there are many different factors brought into play; it has become an iconic image.

Da Vinci fame grew during his lifetime, though he was not a wealthy man and he had to rely on the patronage of his patrons. This included powerful men, such as Cesare Borgia, who in the early 1500s demanded Da Vinci design instruments of war. Da Vinci designed a crossbow, prototype tank and ‘machine gun.’

Personal life of Da Vinci

Leonardo remained single throughout his life. He did not marry or have children. He kept his personal life private and shared few details. He was close with his pupils Salai and Melzi, but appeared to be mostly absorbed in his far-reaching investigations, work and paintings. In his day, contemporary reports indicated Da Vinci was a unique person, with a physical beauty, dignified presence and strong moral character. Da Vinci expresses his love of truth:

“To lie is so vile, that even if it were in speaking well of godly things it would take off something from God’s grace; and Truth is so excellent, that if it praises but small things they become noble.” The Notebooks of Leonardo da Vinci

His first biographer, Giorgio Vasari, writes on the person of Da Vinci in 1550.

“..Besides a beauty of body never sufficiently extolled, there was an infinite grace in all his actions; and so great was his genius, and such its growth, that to whatever difficulties he turned his mind, he solved them with ease.” (Source text)

A notable characteristic of Da Vinci was his wide-ranging respect and reverence for truth, life and living creatures. He adopted a vegetarian diet and would buy caged birds just so he could release them. He is quoted as saying:

“The time will come when men such as I will look upon the murder of animals as they now look upon the murder of men.”

Between 1506-1510, Leonardo spent time in Milan working on behalf of the very generous French King Lois XII. In 1513 he travelled to the Vatican, Rome where he enjoyed the patronage of the new Medici Pope, Leo X. Here, Da Vinci worked in proximity to contemporaries such as the great Masters Michelangeloand Raphael. However, an intense rivalry soon developed between the younger Michelangelo and Da Vinci.

The religion of Da Vinci

Despite being the patron of the Pope, Da Vinci was not an orthodox Catholic. Vasari writes of Da Vinci that he was:

“cast of mind was so heretical that he did not adhere to any religion, thinking perhaps that it was better to be a philosopher than a Christian.”

Madonna of the Rocks (cropped) by Da Vinci

Vasari removed this quote in the second edition but, from his life’s work, we can see Da Vinci valued reason and was willing to question dogma passed down through the ages. Da Vinci wrote criticisms of the sale of indulgences by the Catholic Church. The religious paintings of Da Vinci also indicate a religious faith expressed in a non-conformist way. His Madonna on the Rocks incorporates a Virgin Mary, not dressed regally or surrounded with a halo, but simply dressed in the surroundings of nature. Da Vinci did believe in God, but his religious sensibilities were expressed through seeing God in art, science and nature.

“We, by our arts may be called the grandsons of God.” The Notebooks of Leonardo da Vinci

Da Vinci was a great perfectionist – one reason why he completed so few paintings was that he never felt he had satisfactorily finished anything. He said towards the end of his life:

“I have offended God and mankind because my work didn’t reach the quality it should have.”

In 1515, Da Vinci left to settle at the castle of Cloux, near Amboise by the kind invitation of Francis I of France. Here Da Vinci, spent his remaining years, free to pursue his own studies. He died in 1519 leaving behind one of the greatest body of artistic and scientific works.

Citation: Pettinger, Tejvan.

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“Father of Geometry”: EUCLID, The Mathematician

Euclid (c. 325 BC – 265 BC) – Greek Mathematician considered the “Father of Geometry”. His textbook ‘Elements’ remained a highly influential mathematics teaching book until the late 19th Century and is one of the most widely published books in the world. It has had a lasting influence on the sciences -, especially in mathematics. In a list by Michael H. Hast – Euclid is considered to be 14th most influential person in history.

Euclid was born in the mid 4th Century BC and lived in Alexandria; he was mostly active during the reign of Ptolemy I (323-283BC) His name Euclid means “renowned, glorious” – he is also referred to as Euclid of Alexandria.

Details about Euclid’s life are sparse – the main biographical information was not written until many centuries later, e.g. Proclus c. 450 AD. Proclus writes about Euclid:

“Not much younger than these [pupils of Plato] is Euclid, who put together the “Elements”, arranging in order many of Eudoxus’s theorems, perfecting many of Theaetetus’s, and also bringing to irrefutable demonstration the things which had been only loosely proved by his predecessors. This man lived in the time of the first Ptolemy; for Archimedes, who followed closely upon the first Ptolemy makes mention of Euclid, and further they say that Ptolemy once asked him if there were a shorted way to study geometry than the Elements, to which he replied that there was no royal road to geometry.”

It is likely Euclid worked with a team of mathematics in Alexandria and he received a degree of help in his mathematical works. Some historians feel the works of Euclid may have been the result of several authors, but most agree that one person – Euclid – was the principal author.

It is likely that Euclid would have studied at Plato’s Academy in Athens and much of his initial knowledge would have come from this Plato perspective. In particular, Euclid would have learnt much geometry from Eudoxus.

Another later historian – Pappus writes on Euclid (in 320 AD) that Euclid was of good character, stating – that Euclid was:

“.. most fair and well disposed towards all who were able in any measure to advance mathematics, careful in no way to give offence, and although an exact scholar not vaunting himself.”

Although little is known for certain about Euclid’s personal life, his main book ‘The Elements’(originally written in ancient Greek) became a standard work of important mathematical teachings. It is divided into 13 books.

• Books one to six deal with plane geometry.
• Books seven to nine deal with number theory
• Book eight is on geometrical progression
• Book ten deals with irrational numbers and
• Books eleven to thirteen deal with three-dimensional geometry.

Euclid’s genius was to take the many different diverse elements of mathematical ideas in circulation and combine into one logical, coherent format.

Euclid’s Elements from Weston Library Oxford

Some of the most influential aspects of Euclid include

• His work on prime numbers
• Euclid’s lemma – which states a fundamental property of prime numbers is that – If a prime divides the product of two numbers, it must divide at least one of those numbers.
• The fundamental theorem of arithmetic or the unique-prime-factorization theorem. Using Euclid’s lemma,  this theorem states that every integer greater than one is either itself a prime or the product of prime numbers and that there is a definite order to primes.

“If two numbers by multiplying one another make some number, and any prime number measure the product, it will also measure one of the original numbers.”

— Euclid, Elements Book VII, Proposition 30

• Euclidean algorithm – an efficient method for computing the greatest common divisor (GCD) of two numbers, the largest number that divides both of them without leaving a remainder.
• Geometry. Euclid described a system of geometry concerned with shape, and relative positions and properties of space. It was Euclid who put geometry into axiomatic forms (logically derived theorems) His work is known as Euclidean geometry.

It is sometimes said that, next to the Bible, the “Elements” may be the most translated, published, and studied of all the books produced in the Western world.

Some have stated that ‘The Elements‘ by Euclid may be the second most published, translated and studied of all books, after the Bible.

Apart from the influential Elements, Euclid investigated other branches of mathematics.

Optics – Euclid investigated the apparent size of an object compared to its distance from the eye. Proposition 45 stated that for objects of any two unequal sizes, there is a point from which the two appear equal.

Phaenomena – A work on Spherical geometry  – observing objects in space and using geometry to create measurements

Division of Figures – dividing figures into more constituent parts.

Data – Looking at the given information from geometrical problems.

Citation: Pettinger, Tejvan. 

PUBLICATION: Omotoso Ibukunoluwa

The man called Aristotle

Aristotle (384BC – 322BC) A Greek philosopher, natural scientist and polymath, who made extensive studies into the world around us. Aristotle’s investigations and studies developed the foundations for Western intellectual studies. His writings formed the basis for much knowledge of the first Millennium.

“Time crumbles things; everything grows old under the power of Time and is forgotten through the lapse of Time.”

– Aristotle (Physics)

Living in the same time period as Platoand Alexander the Great, Aristotle helped lay the foundations for western civilisation through his wide range of intellectual and scientific studies.

Aristotle was one of the great polymaths of his time. He studied under Plato and therefore learnt much about the great philosophic traditions of Socrates. But, Aristotle was more than just a good student; he had an independent mind and was able to question many different things and sought to resolve difficult questions and previously unsolvable problems. He made studies in botany, physics, philosophy, logic, and was well known for being a powerful lecturer and debater. He was also regarded as a kindly man, compassionate to others.

In the field of physics, Aristotle’s ideas influenced much of the medieval period and lasted into the European Renaissance. His ideas were later replaced by the physics of Isaac Newton.

Aristotle believed in the power of reason to illuminate the problems of man. He believed that man had the capacity for enlightenment through self-inquiry and study. He believed that human goodness derived from rational thought. Aristotle was also a playwright and he described how the weakness of man – pride, anger, jealousy, could lead to his downfall.

“Piety requires us to honor truth above our friends.”

– Aristotle (Nicomachean Ethics)

Aristotle was also the teacher of the future Macedonian King – Alexander the Great. Aristotle taught the future king, political philosophy, history and ethics. Alexander the Great was to ignore much of Aristotle’s teachings such as the desirability of oligarchic leadership, but, his education by Aristotle must have left an abiding impression on the young prince.

“If liberty and equality, as is thought by some, are chiefly to be found in democracy, they will be best attained when all persons alike share in the government to the utmost.”

– Aristotle (Politics)

Aristotle’s work Politics is an attempt at a practical philosophy to allow justice and freedom. He also saw politics as a method of ensuring man had the capacity to live harmoniously and allow him to pursue noble ideas.

“The political partnership must be regarded, therefore, as being for the sake of noble actions, not for the sake of living together.”

In addition to the above interests, Aristotle pioneered the study of zoology, logic and helped in the development of medicine, optics, and ethics.

“One swallow does not make a summer, nor does one day; and so too one day, or a short time, does not make a man blessed and happy. ”

– Aristotle (Nicomachean Ethics)

Aristotle was one of the few classical philosophers who strongly influenced later Christian writers such as Thomas Aquinas.

SOURCE

Citation: Pettinger, Tejvan. 

PUBLICATION: Omotoso Ibukunoluwa Omoniyi